{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/OJB-Quantum/Maxwell-Boltzmann-Distribution/blob/main/blackbody_radiation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "d9a0c591-e266-44b1-97cf-0386acfba9b1",
      "metadata": {
        "id": "d9a0c591-e266-44b1-97cf-0386acfba9b1"
      },
      "outputs": [],
      "source": [
        "# To run this code numpy and matplotlib are needed. To install them use\n",
        "# pip install numpy matplotlib\n",
        "# In the case this doesn't work, try\n",
        "# pip3 install numpy matplotlib\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "fc79b157-d508-48a8-b328-687683618c14",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fc79b157-d508-48a8-b328-687683618c14",
        "outputId": "7744f598-ece3-47e7-89c1-7faf2569d267"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-7-aad55cfe0292>:28: RuntimeWarning: overflow encountered in exp\n",
            "  return (2 * h * c**2) / (wavelength ** 5 * (np.exp(exponent) - 1))\n",
            "<ipython-input-7-aad55cfe0292>:32: RuntimeWarning: overflow encountered in exp\n",
            "  return (8 * np.pi * h * c) / (wavelength ** 5 * (np.exp(exponent) - 1))  # Write this down\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Constants\n",
        "c = 3.0e8           # Speed of light in vacuum (m/s)\n",
        "h = 6.626e-34       # Planck's constant (J*s)\n",
        "k_B = 1.381e-23     # Boltzmann constant (J/K)\n",
        "T = 100    # Temperature in Kelvin (K). Gap steps used is 580. Change from 100 to 3000 kelvin for the submission. It might be a good idea to use a for loop function. The default script uses 4000 degree Kelvin.\n",
        "# [100, 680, 1260, 1840, 2420, 3000]\n",
        "\n",
        "# Wavelength range (in meters)\n",
        "l_min = 1e-9\n",
        "l_max = 3.0e-6\n",
        "wavelength = np.linspace(l_min, l_max, 1000)  # from 1 nm to 3 µm\n",
        "#wavelength = np.linspace(1e-9, 3e-6, 1000)\n",
        "\n",
        "# Rayleigh-Jeans law (spectral radiation)\n",
        "def rayleigh_jeans_radiance(wavelength, T):\n",
        "    return (2 * c * k_B * T) / (wavelength ** 4)\n",
        "\n",
        "# Rayleigh-Jeans law (spectral density)\n",
        "def rayleigh_jeans_density(wavelength, T):\n",
        "    return (8 * np.pi * k_B * T) / (wavelength ** 4) # Write this down\n",
        "\n",
        "# Planck's law (radiance)\n",
        "def planck_law_radiance(wavelength, T):\n",
        "    exponent = h * c / (wavelength * k_B * T)\n",
        "    return (2 * h * c**2) / (wavelength ** 5 * (np.exp(exponent) - 1))\n",
        "\n",
        "def planck_law_density(wavelength, T):\n",
        "    exponent = h * c / (wavelength * k_B * T)\n",
        "    return (8 * np.pi * h * c) / (wavelength ** 5 * (np.exp(exponent) - 1))  # Write this down\n",
        "\n",
        "# Spectral radiance\n",
        "rj_radiance = rayleigh_jeans_radiance(wavelength, T)\n",
        "planck_radiance = planck_law_radiance(wavelength, T)\n",
        "\n",
        "# Spectral density\n",
        "rj_density = rayleigh_jeans_density(wavelength, T)\n",
        "planck_density = planck_law_density(wavelength, T)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "c335f13a-d60f-4ef5-b425-ea62a599d4d7",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "c335f13a-d60f-4ef5-b425-ea62a599d4d7",
        "outputId": "877f1b5a-2f0a-4f46-e609-ae3ce9a2011a"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plotting\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(wavelength * 1e9, rj_radiance, label='Rayleigh-Jeans Law', linestyle='--')\n",
        "plt.plot(wavelength * 1e9, planck_radiance, label=\"Planck's Law\", color='red')\n",
        "plt.ylim(0,15e12)\n",
        "plt.xlim(l_min*1e6,l_max*1e9)\n",
        "plt.xlabel('Wavelength (nm)')\n",
        "plt.ylabel('Spectral Radiance (W/m^2/sr/m)')\n",
        "plt.title(f'Spectral radiance T = {T} K')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "6afcc361-58fd-436f-ad2d-1cf3c6601ab5",
      "metadata": {
        "id": "6afcc361-58fd-436f-ad2d-1cf3c6601ab5",
        "outputId": "803c0fb6-ed95-4f45-eaeb-1dc7777d7907",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plotting\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(wavelength * 1e9, rj_density, label='Rayleigh-Jeans Law', linestyle='--')\n",
        "plt.plot(wavelength * 1e9, planck_density, label=\"Planck's Law\", color='red')\n",
        "plt.ylim(0,2e5)\n",
        "plt.xlim(l_min*1e6,3000)\n",
        "plt.xlabel('Wavelength (nm)')\n",
        "plt.ylabel('Spectral Radiance (W/m^2/sr/m)')\n",
        "plt.title(f'Spectral density T = {T} K')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "66f01be2-3d8b-410e-af3b-7a2eeb553b0a",
      "metadata": {
        "id": "66f01be2-3d8b-410e-af3b-7a2eeb553b0a"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.12"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}